Results 81 to 90 of about 5,037 (196)
Ground states of a non‐local variational problem and Thomas–Fermi limit for the Choquard equation
Journal of the London Mathematical Society, Volume 111, Issue 3, March 2025.Abstract We study non‐negative optimisers of a Gagliardo–Nirenberg‐type inequality ∫∫RN×RN|u(x)|p|u(y)|p|x−y|N−αdxdy⩽C∫RN|u|2dxpθ∫RN|u|qdx2p(1−θ)/q,$$\begin{align*} & \iint\nolimits _{\mathbb {R}^N \times \mathbb {R}^N} \frac{|u(x)|^p\,|u(y)|^p}{|x - y|^{N-\alpha }} dx\, dy\\ &\quad \leqslant C{\left(\int _{{\mathbb {R}}^N}|u|^2 dx\right)}^{p\theta } {\
Damiano Greco +3 more
wiley +1 more source
Global second‐order estimates in anisotropic elliptic problems
Proceedings of the London Mathematical Society, Volume 130, Issue 3, March 2025.Abstract This work deals with boundary value problems for second‐order nonlinear elliptic equations in divergence form, which emerge as Euler–Lagrange equations of integral functionals of the Calculus of Variations built upon possibly anisotropic norms of the gradient of trial functions.
Carlo Alberto Antonini +4 more
wiley +1 more source
A weighted Hardy-Sobolev-Maz’ya inequality
, 2014 We provide a weighted extension of a Hardy-Sobolev-Maz’ya inequality that is due to Filippas, Maz’ya and ...
Sourdis, Christos
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Persistence of the solution to the Euler equations in an end‐point critical Triebel–Lizorkin space
Mathematical Methods in the Applied Sciences, Volume 48, Issue 2, Page 2421-2433, 30 January 2025.Local stay of the solutions to the Euler equations for an ideal incompressible fluid in the end‐point Triebel–Lizorkin space F1,∞sℝd$$ {F}_{1,\infty}^s\left({\mathbb{R}}^d\right) $$ with s≥d+1$$ s\ge d+1 $$ is clarified.
JunSeok Hwang, Hee Chul Pak
wiley +1 more source
Advances in Nonlinear Analysis, 2019 The paper is concerned with the existence and multiplicity of positive solutions of the nonhomogeneous Choquard equation over an annular type bounded domain.
Goel Divya, Sreenadh Konijeti
doaj +1 more source
Effective upper bounds on the number of resonances in potential scattering
Mathematika, Volume 71, Issue 1, January 2025.Abstract We prove upper bounds on the number of resonances and eigenvalues of Schrödinger operators −Δ+V$-\Delta +V$ with complex‐valued potentials, where d⩾3$d\geqslant 3$ is odd. The novel feature of our upper bounds is that they are effective, in the sense that they only depend on an exponentially weighted norm of V.
Jean‐Claude Cuenin
wiley +1 more source
Advances in Nonlinear AnalysisIn this study, we explore the positive solutions of a nonlinear Choquard equation involving the Green kernel of the fractional operator (−ΔBN)−α⁄2{\left(-{\Delta }_{{{\mathbb{B}}}^{N}})}^{-\alpha /2} in the hyperbolic space, where ΔBN{\Delta }_{{{\mathbb{
Gupta Diksha, Sreenadh Konijeti
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Electronic Journal of Qualitative Theory of Differential EquationsIn this paper, we study the following Choquard-Kirchhoff type equation $$ \left( a+b\|u\|^{p(\theta-1)}\right) \left( -\Delta_{p}u+(-\Delta)^{s}_{p}u\right) =\left( \int_{\mathbb R^N}\frac{|u(y)|^{p_{\mu}^{*}}}{|x-y|^\mu}dy\right) |u|^{p_{\mu}^{*}-2}u+\
Wenjing Chen, Jingran Feng
doaj +1 more source
Abstract and Applied Analysis, Volume 2025, Issue 1, 2025.This paper is concerned with the positive solutions to a fractional‐order system with Hartree‐type nonlinearity and its equivalent integral system. We firstly use the regularity lifting lemma to obtain the integrability and smoothness of the solutions.
Yu-Cheng An +2 more
wiley +1 more source
The Hardy-Littlewood Inequality for the Solution to P-Harmonic Type System
, 2011 [[abstract]]Hardy-Littlewood inequality is instrumental in virtually all analytic aspects of the theory of partial differential equations, linear and nonlinear.
Ronglu Li +4 more
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